# Symmetry analysis for a fourth-order noise-reduction partial differential equation

@article{Leach2020SymmetryAF, title={Symmetry analysis for a fourth-order noise-reduction partial differential equation}, author={P. G. L. Leach and Andronikos Paliathanasis}, journal={Quaestiones Mathematicae}, year={2020}, volume={44}, pages={1541 - 1552} }

Abstract We apply the theory of Lie symmetries in order to study a fourth-order 1+2 evolutionary partial diﬀerential equation which has been proposed for the image processing noise reduction. In particular we determine the Lie point symmetries for the specific 1+2 partial diﬀerential equations and we apply the invariant functions to determine similarity solutions. For the static solutions we observe that the reduced fourth-order ordinary diﬀerential equations are reduced to second-order…

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